Question: Simplify the following expression: $ q = \dfrac{a + 9}{-2a} - \dfrac{-9}{7} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{a + 9}{-2a} \times \dfrac{7}{7} = \dfrac{7a + 63}{-14a} $ Multiply the second expression by $\dfrac{-2a}{-2a}$ $ \dfrac{-9}{7} \times \dfrac{-2a}{-2a} = \dfrac{18a}{-14a} $ Therefore $ q = \dfrac{7a + 63}{-14a} - \dfrac{18a}{-14a} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{7a + 63 - 18a }{-14a} $ Distribute the negative sign: $q = \dfrac{7a + 63 - 18a}{-14a}$ $q = \dfrac{-11a + 63}{-14a}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{11a - 63}{14a}$